Multiple bubble dynamics and velocity selection in Laplacian growth without surface tension

Abstract

A new selection phenomenon in nonlinear interface dynamics is predicted. A generic class of exact regular unsteady multi-bubble solutions in a Hele-Shaw cell is presented. These solutions show that the case where the asymptotic bubble velocity, $U$, is twice greater than the velocity, $V$, of the uniform background flow, i.e., $U=2V$, is the only attractor of the dynamics. Contrary to common belief, the predicted velocity selection requires neither surface tension nor other external regularization.

27 pages, 1 figure. Final published version

References in corpus (3)

• Saffman-Taylor streamers: mutual finger interaction in an electric breakdown
• Random Matrices in 2D, Laplacian Growth and Operator Theory
• Multiple bubbles and fingers in a Hele-Shaw channel: complete set of steady solutions